How do I mark all critical points on a graph of a function?

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I'm trying to plot the function f=(sin(x)+(1/3)*(cos(5*x))) across 0<=x<=2pi, find all roots of the derivative and then use them to mark all the critical points on the graph. The following code is as far as I've got:
syms x;
f=(sin(x)+(1/3)*(cos(5*x)));
v=diff(f)
fplot(f,[0 10])
hold on
fplot(v,[0 10])
roots(v)
I've tried the solve command too but cannot find a way to list all roots, plug the roots into the original function, then mark the resultant critical points on the graph.
Any advice appreciated, thanks.

Accepted Answer

Matt J
Matt J on 18 Feb 2024
Edited: Matt J on 18 Feb 2024
syms x;
f=(sin(x)+(1/3)*(cos(5*x)));
v=matlabFunction( diff(f) );
f=matlabFunction(f);
x=linspace(0,2*pi,1e5);
loc=find(gradient(sign(v(x)))~=0);
xcrit=mean(reshape(x(loc),2,[])); %critical point x-coordinates
fplot(f,[0 2*pi])
hold on
plot(xcrit,f(xcrit),'rx')
hold off;
legend('f(x)', 'crit points','Location','NE'); axis padded
  2 Comments
Lincoln
Lincoln on 18 Feb 2024
Wow thanks! Is there a way I can find the roots of a derivative function and store them as an array?

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